Users of the Apple iPhone, iPad or iPod Touch are commonly experiencing “Not Delivered” messages appearing when they try to use iMessage. This problem seems to be related to the DNS configuration on certain networks. Internet providers may not have things setup correctly while others may intentionally block iMessage traffic.
To work around this issue, you may want to try changing the DNS settings on your device to utilize Google’s public DNS.
1. Open Settings.
2. Select Wi-Fi.
3. Tap arrow next to the wireless connection you are using.
4. Tap the DNS field and remove any data that already exists in the field, then type 188.8.131.52, 184.108.40.206
Once you are finished, press the Home button and give iMessage another try. This fix has worked for many users and I hope it works the same for you.
Note: If you have access to the wireless router you are connecting your device to, you may want to set the DNS settings there.